Rheological Model for Simulation of Hot rolling of New Generation Steel Strips for Automotive Applications

The main objective of this paper is the development of a rheological model for automotive steels for the conditions of hot strip rolling and implementation of this model in a finite element program is. Three types of steels were investigated, IF, dual phase and TRIP steel. Plastometric tests were performed on a Gleeble 3800 simulator for the temperature range 850‐1200°C and strain rates 3‐150 s^?1. Inverse analysis was applied to eliminate the influence of disturbances occurring in the plastometric tests and to determine the real flow stress of the material. The coefficients in the flow stress equation were evaluated and this equation was implemented in the FEM code as the constitutive law. The model was validated by comparison of measured and calculated loads in the compression tests and by strip rolling experiments conducted in the laboratory mill. Validation confirmed a good predictive capability of the rheological model.     

Validation of a Model of Plastic Deformation of C‐Mn Steels in the Two‐Phase Temperature Region

The paper describes the validation of a thermal‐mechanical‐microstructural model of deformation of carbon‐manganese steels in the two‐phase temperature region. The model has been developed on the basis of dilatometric and plastometric tests performed for a wide range of temperatures and strain rates. Dilatometric tests were used to identify the phase transformation model and plastometric tests were used to identify the flow stress model. Inverse analysis was applied to find the parameters of the models which were further implemented into a finite element code. Numerical simulations of the deformation of steels in the two‐phase temperature range were performed. Multi‐stage plane strain compression tests were performed to validate the model. The samples were quenched after subsequent stages of the tests and metallographic analysis was performed. Predicted loads, grain size and volume fractions of the microstructural components were compared with measurements and the coefficients in the models were updated.     

Identification of Rheological Parameters on the Basis of Various Types of Compression and Tension Tests

The objective of the project was to determine flow stress on the basis of various plastometric tests. The experiments used uniaxial compression, ring compression, and plane strain compression for two sizes of samples and tensile tests. The material was carbon‐manganese steel, and all the tests were performed at three temperatures (900, 1000, and 1100°C) and at three strain rates for each temperature (0.1, 1, and 10 s^?1). Inverse analysis was applied to the interpretation of the results of all compression tests. The flow stresses obtained from various compression tests were compared resulting in the following observations: consistent results between the tests were observed for low values of the Zener‐Hollomon parameter, but some discrepancies appeared for larger values of this parameter. The sensitivity of the results of inverse analysis with respect to the friction factor was investigated next, and it was concluded that the flow stress determined from ring compression showed the largest sensitivity to friction. This sensitivity was lower for uniaxial compression and plane strain compression of small samples, and no sensitivity was observed for plane strain compression of large samples. Finally, the simulations of the tensile tests were performed using the rheological models determined in compression, and reasonably good results were obtained.     

Computer Aided Design of New Forging Technology for Crank Shafts

Application of numerical simulations to improve forging technology for crank shafts is the objective of this work. Plastometric tests were performed for steels used for manufacturing of crank shafts and a rheological model for these steels was determined. Inverse analysis was applied for the identification of the model parameters. This model was implemented in the finite element software and simulations of various variants of forging were performed. Results of simulations were used to select the best variant, which gives the lowest loses of the material and proper shape of the final product.     

Inverse Analysis of Tensile Tests

Application of the inverse analysis to the interpretation of hot tensile tests is the main objective of the work. Tensile tests were performed for carbon‐manganese steel samples at 1000°C and at three ram velocities. The measured temperature distribution was used as boundary condition in the finite element model of the direct problem. Recorded loads and elongation of the sample were used as input for the inverse analysis. The flow stress, recalculated for isothermal conditions and constant strain rate deformation, was determined as a function of strain up to the maximum deformations achieved in the neck. Validation of the flow stress model based on comparison of the measured loads with the finite element predictions for the developed Theological model, confirmed reasonably good accuracy of the procedure. Additionally, sensitivity of the measured parameters (loads and radius of the neck at certain elongation) with respect to the rheological parameters has been performed.     

Validation of a Model of Plastic Deformation of Niobium Microalloyed Steels in the Two‐Phase Temperature Region

This article describes a thermo‐mechanical‐microstructural model for deformation of niobium microalloyed steel in the two‐phase range of temperatures. Results of physical and numerical modeling are presented. The physical simulation experiments include plastometric and dilatometric tests, as well as industrial rolling trial. Plastometric tests were performed to describe the flow stress for the wide range of temperatures, including ferritic, two‐phase, and austenitic states. Two‐stage deformation tests were performed to identify the microstructure evolution model. Dilatometric tests were used to identify the model of phase transformation. A model of the kinetics of the precipitation was adapted from the literature. The coefficients in all the models were identified using inverse analysis. Developed models were implemented in the finite element code. In order to improve the accuracy of the flow stress predictions in the two‐phase phase temperature range, internal variable dislocation density model was included, as well. The proposed combination of models correctly predicted microstructure changes and mechanical properties in the two‐phase range, during the transformations of the thermo‐mechanical treatment. Industrial trials were performed for the final validation of the models.     

Computer Modelling of Deformation of Steel Samples with Mushy Zone

The integrated casting and rolling of steel plates in processes such as Inline Strip Production or Arvedi Steel Technology is the latest and very efficient way of hot strip production. The numerical modelling is very helpful in developing a “know how” theory for the mentioned processes. One of the most important relationships having crucial influence on the metal flow path is the strain‐stress curve. The inverse method, which is usually the only method of calculating a real strain‐stress relationship, needs a good mathematical model describing the plastic behaviour of the material. The model presented in the current paper fills the gap in modelling of plastic deformation of semi‐solid materials. On the other hand, the mathematical modelling should be closely related to experiments. The well known machine allowing tests in the discussed temperature range is the GLEEBLE thermo‐mechanical simulator. However, carrying out experiments with steel deformation in the semi‐solid state using this machine is very expensive. Therefore, application of a dedicated computer simulation system is strictly required. Inverse analysis and appropriate modelling of the testing procedure makes tests possible, first of all, but it also results in lowering testing cost. The newest version of the Def_Semi_Solid is a unique FEM system supporting tests at extra high temperature.     

A Model Based on the Assessment of Intrinsic Creep Resistance Concept

In the present study a simple model is proposed to assess creep behavior. The model is applied to experimental results performed on austenitic steel X8 CrNiMoNb 16 16. The model is based on a modification of the Levy‐Mises equation for plasticity to consider creep time effects, introducing as a parameter the intrinsic creep resistance. The assessment of creep behavior applied for monotonic and two stages loading data is good. The model could assess negative creep strain rates as well as damage accumulation observed as an increase of the minimum creep rate after each reloading at the same stress level in two stages tests.     

Dislocation mechanics-based constitutive equations

A review of constitutive models based on the mechanics of dislocation motion is presented, with focus on the models of Zerilli and Armstrong and the critical influence of Armstrong on their development. The models were intended to be as simple as possible while still reproducing the behavior of real metals. The key feature of these models is their basis in the thermal activation theory propounded by Eyring in the 1930’s. The motion of dislocations is governed by thermal activation over potential barriers produced by obstacles, which may be the crystal lattice itself or other dislocations or defects. Typically, in bcc metals, the dislocation-lattice interaction is predominant, while in fcc metals, the dislocation-dislocation interaction is the most significant. When the dislocation-lattice interaction is predominant, the yield stress is temperature and strain rate sensitive, with essentially athermal strain hardening. When the dislocation-dislocation interaction is predominant, the yield stress is athermal, with a large temperature and rate sensitive strain hardening. In both cases, a significant part of the athermal stress is accounted for by grain size effects, and, in some materials, by the effects of deformation twinning. In addition, some simple strain hardening models are described, starting from a differential equation describing creation and annihilation of mobile dislocations. Finally, an application of thermal activation theory to polymeric materials is described. This article is based on a presentation given in the symposium “Dynamic Deformation: Constitutive Modeling, Grain Size, and Other Effects: In Honor of Prof. Ronald W. Armstrong,” March 2–6, 2003, at the 2003 TMS/ASM Annual Meeting, San Diego, California, under the auspices of the TMS/ASM Joint Mechanical Behavior of Materials Committee.     

Prediction of gas‐liquid two‐phase mixture flow in a vertical pipe with a sudden expansion in diameter

The principle of gas‐lift pumps is applied to vacuum‐decarburization with the RH (Ruhrstahl Heraeus) process to circulate molten steel. Gas‐lift pumps are also applicable to the transportation of molten iron/steel between different refining processes. This paper treats theoretical analysis of steady‐state flow characteristics of gas‐liquid two‐phase mixtures rising in a vertical pipe with an abrupt expansion of its diameter. The system of governing equations is based upon a one‐dimensional multi‐fluid model. Flow pattern transitions are taken into consideration. A new numerical procedure to predict the flow characteristics at the sudden expansion has been proposed. Experiments have also been performed for several conditions to confirm the applicability as well as the validity of the present numerical model. It has been found that the predictions agree reasonably well with the experimental data. Next, the effect of the sudden expansion of pipe diameter on the pump performance was investigated numerically. As a result, it has been confirmed that the sudden expansion of pipe diameter contributes to improve the pump efficiency.     

Determination of Flow Curve and Plastic Anisotropy of Medium-thick Metal Plate: Experiments and Inverse Analysis

Sheet bulk metal forming is widely used for medium-thick metal plate due to its convenience in the manufacture of accurately finished 3Dfunctional components.To obtain precise anisotropy and flow curve of metal plate is aprerequisite for correct simulation of sheet bulk metal forming processes.Inverse analysis of compression test was introduced here to evaluate the sensitivity of different flow curve models and geometric influence of compression test specimen.Besides,a methodology was proposed to compute plastic anisotropic coefficients of Hill quadratic yield criterion,which is based on the ratios of flow curves obtained by inverse analysis of compression tests using specimens cut in six directions on the medium-thick metal plate.The obtained flow curves and anisotropic coefficients were compared with those calculated from tensile tests.Flow curves based on inverse analysis of compression tests cover the curves of the tensile tests well,while the anisotropic coefficients are different,especially for the coefficient related to the RT45 direction.To estimate the effectiveness of the proposed method,the calculated material properties and those based on the traditional tensile tests were applied in a rim-hole process simulation.The simulation results based on the material properties from inverse analysis of compression tests accorded with the tested properties better.     

Modeling of Mechanical Characteristics in Hot Deformation of 4130 Steel

In this investigation, hot compression tests were performed at 900 °C ? 1100 °C and strain rate of 0.001 ? 0.1 s^?1 to study hot deformation behavior and flow stress model of 4130 steel. Based on the classical stress–dislocation relations and the kinematics of the dynamic recrystallization, the flow stress constitutive equations of the work hardening‐dynamical recovery period and dynamical recrystallization period were established for 4130 steel, respectively. The validity of the model was demonstrated by comparing the experimental data with the numerical results. The agreement of this comparison is quite reasonable.     

Conventional and Multiscale Modeling of Microstructure Evolution During Laminar Cooling of DP Steel Strips

Physical and numerical simulations of the hot rolling and laminar cooling of DP steel strips are presented in the paper. The objectives of the paper were twofold. Physical simulations of hot plastic deformation were used to identify and validate numerical models. Validated models were applied to simulate the manufacturing of DP steel strips. Conventional flow stress model and microstructure evolution model were used in the hot deformation part. The approach to the complex systems analysis based on global thermodynamic characterization and detailed microstructure characterization was applied to determine equilibrium state at various temperatures. Finally, two numerical models were used to simulate kinetics of austenite decomposition at varying temperatures: the first, conventional model based on the Avrami equation, and the second, the discrete Cellular Automata approach. Plastometric tests and stress relaxation tests were used for identification of the hot rolling model for the DP steel. Dilatometric tests were performed to identify the phase transformation models. Verification confirmed good accuracy of all models. Validated models were applied to simulate the manufacturing of DP steel strips. Influence of technological parameters (e.g., strip thickness and velocity, active sections in the laminar cooling, and water flux in the sections) on the DP microstructure was analyzed. The cooling schedules, which give required microstructures were proposed. The numerical tool, which simulates manufacturing chain for DP steel strips is the main output of the paper.     

Three-Dimensional Numerical Study of Flows in Open-Channel Junctions

An open-channel junction flow is encountered in many hydraulic structures ranging from wastewater treatment facilities to fish passage conveyance structures. An extensive number of experimental studies have been conducted but a comprehensive three-dimensional numerical study of junction flow characteristics has not been performed and reported. In this paper, a three-dimensional numerical model is developed to investigate the open-channel junction flow. The main objective is to present the validation of a three-dimensional numerical model with high-quality experimental data and compare additional simulations with classical one-dimensional water surface calculations. The three-dimensional model is first validated using the experimental data of a 90° junction flow under two flow conditions. Good agreement is obtained between the model simulation and the experimental measurements. The model is then applied to investigate the effect of the junction angle on the flow characteristics and a discussion of the results is presented.     

Behavior of model Fe-Ni-Cr alloys during stress-rupture in sulfidizing and oxidizing environments

Stress-rupture tests of model Fe-Ni-Cr alloys have been performed at 815 °C in gaseous environments containing multiple oxidants (O, S, C). The decrease in stress-rupture lifetime, when present, was the result of an accelerated onset of tertiary creep brought about by environment related surface cracking. Secondary creep rates were not significantly affected. The applied stress was found to increase the depth of environmental attack but it did not alter the morphology of attack. Penetration depths were modeled using a diffusion analysis which included both bulk and grain boundary diffusion.     

Grain size dependence of the activation parameters for plastic deformation: Influence of crystal structure,slip system,and rate-controlling dislocation mechanism

A critical review of available results on the dependence of grain size on the activation parameters for deformation, specifically, the activation volume, V*, and the thermal component of flow stress, σ*, has been carried out with a view to verifying the Armstrong prediction that identifies the Hall-Petch (H-P) intercept with the easy slip system and the H-P slope with the most difficult system in polycrystals. The influence of slip system choice is demonstrated using results on Cd and Zr. The Armstrong prediction is valid for basal slip hcp metals, such as Cd and Zn, with V* and σ* determined by the difficult pyramidal slip. For the prism slip metals such as Zr and Ti, V* and σ* are controlled by interstitial solutes and are independent of grain size. The results on Zr are used to highlight the influence of dynamic strain aging on the H-P parameters. In bcc metals, in which the Peierls-Nabarro barrier is the rate-controlling obstacle, V* and σ* are again independent of grain size. For fcc metals, correlation of the H-P slope with the cross-slip stress, predicted by the Armstrong model, has been demonstrated for a few cases. The variation of V* with grain size in Ni as reported by Narutani and Takamura (Acta Metall. Mater., 1991, vol. 227, pp. 2037–49) is newly interpreted in terms of the Armstrong model that associates the H-P intercept in fcc metals with dislocation intersections and the H-P slope with cross-slip, and provides realistic results for the activation volumes for the two processes. This article is based on a presentation given in the symposium “Dynamic Deformation: Constitutive Modeling, Grain Size, and Other Effects: In Honor of Prof. Ronald W. Armstrong,” March 2–6, 2003, at the 2003 TMS/ASM Annual Meeting, San Diego, California, under the auspices of the TMS/ASM Joint Mechanical Behavior of Materials Committee.     

Validation of Multi‐scale Model Describing Microstructure Evolution in Steels

Properties of deformed steels depend on various microstructure parameters such as distribution of grain size and precipitates. Strain, strain rate and temperature inhomogeneities make quantitative prediction of microstructure difficult but the Finite Element method is able to model these inhomogeneities. Different scales of phenomena occurring in deformed materials are another difficulty in modelling. Microstructure evolution can be described by more realistic methods (e.g. Cellular Automata CA, Monte Carlo), which, on the other hand, are unable to simulate larger samples. Therefore, development of the methods capable of spanning multiple scales became a current challenge. CAFE modelling, which couples FE and CA methods, is the objective of the paper. The model consists of two layers. The micro‐scale layer, simulated by CA, represents microstructure evolution including nucleation and growth of the grains. Evolution of a dislocation density is described for every grain separately by solving differential equation. The FE thermal‐mechanical model is used as a macro‐scale part. Multistage plane strain compression tests for niobium steel are considered. Distributions of initial and final grain size are measured during the tests. The results from the CAFE model are compared to the measurements and to the predictions by a conventional model. The comparisons confirm the capability of the CAFE method to predict flow stress, recrystallized fraction and grain size distribution. Conventional approach gives a good agreement with experiments for an average grain size only.